Simplify the following expression: $t = \dfrac{z^2 - 8z + 7}{z - 7} $
Explanation: First factor the polynomial in the numerator. $ z^2 - 8z + 7 = (z - 7)(z - 1) $ So we can rewrite the expression as: $t = \dfrac{(z - 7)(z - 1)}{z - 7} $ We can divide the numerator and denominator by $(z - 7)$ on condition that $z \neq 7$ Therefore $t = z - 1; z \neq 7$